Mathematical Research Letters

Volume 18 (2011)

Number 4

Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift

Pages: 613 – 620

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n4.a3

Authors

Ryan Alvarado

Dan Brigham

Vladimir Maz'ya

Marius Mitrea

Elia Ziadé

Abstract

We discuss a sharp generalization of the Hopf–Oleinik boundary point principle (BPP) for domains satisfying an interior pseudo-ball condition, for non-divergence form, semi-elliptic operators with singular drift. In turn, this result is used to derive a version of the strong maximum principle under optimal pointwise blow-up conditions for the coefficients of the differential operator involved. We also explain how a uniform two-sided pseudo-ball condition may be used to provide a purely geometric characterization of Lyapunov domains, and clarify the role this class of domains plays vis-à-vis to the BPP.

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